1. Introduction

The mathematical models representing the nuclear reactor physics are based mainly on two theoretical areas: neutron transport theory and neutron diffusion theory, where it is necessary to remark that neutron diffusion theory is really a simplification of the neutron transport theory.

All the discussions included in this chapter are centered in a simulator for light water reactors. The computer code AZtlan KInetics in Neutron Diffusion (AZKIND) is part of the neutronic codes selected for their implementation in the AZTLAN Platform1 project in which neutron transport and neutron diffusion codes are being developed in Mexico. A (TH) model has been implemented recently and coupled with the neutronic (NK) model, and both models are based

Nuclear Reactor Simulation

7

http://dx.doi.org/10.5772/intechopen.79723

Although there has been growing interest in the transport-based core neutronics analysis methods for a more accurate calculation with high-performance computers, it is yet impractical to apply them in the real core design activities because their performance is not so practical on ordinary desktop or server computing machines. For this reason, most of the neutronics codes for reactor core calculations are still subject to the two-step calculation procedure, which consists of (1) homogenized group neutron parameters generation and (2) neutron diffusion

In the core calculation steps that are the main concern of this work, nodal codes based on the diffusion theory have been used to determine the neutron multiplication factor and the corresponding core neutron flux (or power) distribution. Practically, almost all nuclear reactor simulation codes employ the two-group approach involving only fast and thermal neutron energy groups for the applications to light water reactors (LWR). However, numerical calculations with the two-group structure are not appropriate in the analysis of cores loaded with mixed oxide fuels or analysis of fast breeder reactors, since the neutron spectrum is influenced more by the core environment, requiring much more energy groups than only two groups.

As settled in Ref. [2], even using a high-performance computer, a direct core calculation with several tens of thousands of fuel pins is difficult to perform in its heterogeneous geometry model form, using fine groups of a prepared reactor cross-section library. The Monte Carlo method can handle such a core calculation (see also the Serpent code), but it is not easy to obtain enough accuracy for a local calculation or small reactivity because of accompanying statistical errors, besides the large calculation times. Instead of using neutron transport computer codes, the nuclear design calculation is performed in two steps: (1) lattice calculation in a two-dimensional infinite arrangement of fuel rods or assemblies for the generation of homogenized lattices jointly with their corresponding homogenized cross-sections and (2) core calculation in a three-dimensional whole core, with a neutron diffusion code using the information

As shown in Figure 1 [2], the lattice calculation prepares few-group homogenized cross sections which maintain the energy dependence (neutron spectrum) of nuclear reactions, and these reduce the core calculation cost in terms of time and memory. The final core design

This work was performed under the auspices of the financial support from the National Strategic Project No. 212602

(AZTLAN Platform) as part of the Sectorial Fund for Energetic Sustainability CONACYT—SENER, Mexico.

on HPC implementations.

core calculation.

of the previous step.

1

2. Reactor core calculation overview

Numerical methods are used to solve the partial differential equations representing the nuclear reactor physics, and these methods are derived from discretization techniques. For numerical solutions in any scientific area, computational tools have been developed including software and hardware. In the past, the former computer processing was the sequential execution of computer commands, meaning to say that program tasks are carried out one after one. Modern computational tools have been developed for parallel processing, executing several tasks concurrently.

The computing branch dealing with the system architecture and appropriate software related to the simultaneous execution of computer instructions and applications is known as parallel computing science. Former developments in parallel computing were made in the late 1950s, following the construction of supercomputers throughout the 1960s and 1970s. Nowadays, clusters are the workhorse of scientific computing and are the dominant architecture in data centers.

Since the late 1950s, the performance of safety analyses was essential in the nuclear industry, in research reactors, but mainly safety analyses of nuclear power plants for commercial purposes. Scientific computing calculations were vital to these safety analyses, but with important limitations in computer/computing capabilities. At the beginning, the objective was to give a solution to partial differential equation models based on neutron diffusion or neutron transport with technology and methods available in those years. Numerical techniques were used first with finite differences and finite element approaches, and gradually up to now, with nodal finite element methods (NFEMs). Despite the numerical method employed, the computer code user faces the problem of solving extremely large algebraic systems challenging hardware/ software capabilities. Generation of results for any reactor simulation in considerable short times is a desirable achievement for computer code users [1].

Recent developments of high-performance computer equipment and software have made the use of supercomputing in many scientific areas possible. The appropriate selection of parallel computing software, like newly developed linear algebra libraries, to be used in a specific project may result in a suitable platform to simulate nuclear reactor states with relatively prompt results.

Throughout the world, several research projects in the last decade have been developed with the main objective of making full tridimensional (3D) coupling simulations of nuclear reactor cores, leaving aside the obsolescence of the point kinetics theory. Most of the modern nuclear reactor simulators are based on neutron transport theory, or on neutron diffusion theory, to obtain detailed 3D results. As light water is used for cooling/moderating light water reactors (LWRs), a comprehensive analysis of the reactor core physics must include thermal-hydraulic phenomena, so that modern simulations perform reactor calculations with thermal-hydraulic feedback coupled with neutron kinetics calculations.

All the discussions included in this chapter are centered in a simulator for light water reactors. The computer code AZtlan KInetics in Neutron Diffusion (AZKIND) is part of the neutronic codes selected for their implementation in the AZTLAN Platform1 project in which neutron transport and neutron diffusion codes are being developed in Mexico. A (TH) model has been implemented recently and coupled with the neutronic (NK) model, and both models are based on HPC implementations.
